Demystifying Max Pain

Seeking Alpha contributer Rocco Pendola does an excellent job of explaining max pain. He has posted several interviews with experts where he directly asks about the forces behind max pain. Rocco and the experts agree that hedge unwinding is the major force behind max pain. But the articles themselves are absolutely worth reading.

In the first article, Rocco interviews University of Illinois Professor of Financial Markets and Options Neil Pearson. Neil gives an excellent overview of the hedges established by the option writers.

The second article is an interview with WhatTrading.com Senior Options Strategist Frederic Ruffy. Fred and Rocco openly question if it would even be possible to manipulate a stock to close at max pain.

The following is a excerpt from the Neil Pearson article that describes with an example how pinning and max pain function.

Let’s use AAPL as an example. Friday, AAPL’s closing price was near $340. Further, let’s suppose that there is a large trader or group of traders who follow a hedging strategy that requires them to sell aggressively if AAPL rises above $340, and buy aggressively if AAPL falls below $340. If this is the case, their trading will have a tendency to “pin” AAPL at or near $340. It is only a tendency, because during the week there might be some event, either a news announcement or trading by some other investors, that dwarfs the effect of the hedging strategy and moves AAPL away from $340.

In the explanation above, AAPL pinning at $340 is an incidental byproduct of the hedging strategy. An alternative, more cynical, view is that sometimes some traders will deliberately trade in a way (sell if AAPL rises above $340, fall it AAPL falls below $340) with the intent of pinning AAPL at $340.

I think most pinning is caused by hedge rebalancing, i.e. it is an incidental byproduct of perfectly legal hedging activities. You might wonder, whose hedging? What large trader or traders could possibly be following hedging strategies that cause stock prices to pin? The answer is that delta-hedging trades executed by options market makers can have this effect.

Option market makers often have a lot of natural hedging in their portfolios, e.g. satisfying customer demand might lead them to buy some $55 strike calls, and write some $60 strike calls that partially hedge the $55 strike calls. But this natural hedging is not perfect, and to the extent that it is not, options market makers trade in the underlying stocks to hedge their options positions. When the stock price moves, or as time passes, or when they execute new option trades, they need to rebalance their hedges, that is buy or sell the underlying stock.

Option market makers (and many other options traders) use the concept of option delta in establishing and adjusting their hedges. The option delta is the change in the value of the option or option portfolio resulting from a one dollar change in the price of the underlying stock. For example, on a “per share” basis an at-the-money AAPL call will have a delta of about 0.5. This means that if AAPL moves by $1, say from $339.50 to $340.50, the price of the 340 strike call will change by about $0.50 per share. The value of the option contract on 100 shares will change by about 100 × $0.50 = $50, and the value of say 40 contracts will change by 40 × 100 × $0.50 = $2,000. An option market maker who owns 40 contracts (and no other options) will hedge the position by short-selling 2,000 shares of AAPL. If AAPL falls by $1 the gain of $2,000 on the short position will offset the loss of $2,000 on the options position, while if AAPL rises by $1 the loss of $2,000 on the short position will offset the gain of $2,000 on the options position.

Consider our options market maker who owns 40 calls (on 40 ×100 = 4,000 shares) with a strike of $340, and suppose that AAPL is trading just a bit above $340. The delta of the option position is 2,000, and the market marker will hedge by short-selling 2,000 shares. If AAPL stays above $340 all week until expiration, the call will be exercised, resulting in the purchase of 4,000 shares. Because a stock position of 4,000 shares has a delta of 4,000, the delta of the options position (which, on exercise, becomes a stock position) will increase throughout the week, ending up at 4,000. The delta increases from 2,000 to 4,000 because the calls eventually get exercised, and the call owner receives 4,000 shares. As the option position delta increases from 2,000 to 4,000, the market maker must sell AAPL to increase the short stock position from short 2,000 shares to short 4,000 shares. This has the effect of pushing AAPL down toward $340.

This assumed that AAPL was above $340. If for some reason AAPL drops below $340 and stays below $340, the calls will expire worthless. This means that the options delta will drop to zero at expiration. As expiration approaches, the market maker must maintain a stock position opposite to the option delta. Because the option delta is dropping from 2,000 to zero, the stock position must change from 2,000 short to zero, i.e. the options market maker must buy AAPL to cover the short. This has the effect of pushing AAPL up toward $340.

The effect is that when AAPL is above $340 the hedge rebalancing trades involve selling AAPL, and when AAPL is below $340 the hedge rebalancing trades involve buying AAPL. These trades tend to “pin” AAPL at $340.

In this example, I focused on the change in delta due to the passage of time. Option deltas also change as the stock price moves, leading to an additional source of hedge rebalancing trade. (The change in delta as the stock price changes in known as gamma.) Close to expiration, hedge rebalancing trades due to changes in delta caused by changes in the underlying stock price work in the same direction as hedge rebalancing trades caused by changes in delta as time passes.